Dataset Information

Silhouette width using generalized mean-A flexible method for assessing clustering efficiency.

ABSTRACT: Cluster analysis plays vital role in pattern recognition in several fields of science. Silhouette width is a widely used index for assessing the fit of individual objects in the classification, as well as the quality of clusters and the entire classification. Silhouette combines two clustering criteria, compactness and separation, which imply that spherical cluster shapes are preferred over others-a property that can be seen as a disadvantage in the presence of complex, nonspherical clusters, which is common in real situations. We suggest a generalization of the silhouette width using the generalized mean. By changing the p parameter of the generalized mean between -? and +?, several specific summary statistics, including the minimum, maximum, the arithmetic, harmonic, and geometric means, can be reproduced. Implementing the generalized mean in the calculation of silhouette width allows for changing the sensitivity of the index to compactness versus connectedness. With higher sensitivity to connectedness, the preference of silhouette width toward spherical clusters should reduce. We test the performance of the generalized silhouette width on artificial data sets and on the Iris data set. We examine how classifications with different numbers of clusters prepared by different algorithms are evaluated, if p is set to different values. When p was negative, well-separated clusters achieved high silhouette widths despite their elongated or circular shapes. Positive values of p increased the importance of compactness; hence, the preference toward spherical clusters became even more detectable. With low p, single linkage clustering was deemed the most efficient clustering method, while with higher parameter values the performance of group average, complete linkage, and beta flexible with beta = -0.25 seemed better. The generalized silhouette allows for adjusting the contribution of compactness and connectedness criteria, thus avoiding underestimation of clustering efficiency in the presence of clusters with high internal heterogeneity.

SUBMITTER: Lengyel A

PROVIDER: S-EPMC6912895 | biostudies-literature | 2019 Dec

REPOSITORIES: biostudies-literature

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Silhouette width using generalized mean-A flexible method for assessing clustering efficiency.

Lengyel Attila A Botta-Dukát Zoltán Z

Ecology and evolution 20191119 23

Cluster analysis plays vital role in pattern recognition in several fields of science. Silhouette width is a widely used index for assessing the fit of individual objects in the classification, as well as the quality of clusters and the entire classification. Silhouette combines two clustering criteria, compactness and separation, which imply that spherical cluster shapes are preferred over others-a property that can be seen as a disadvantage in the presence of complex, nonspherical clusters, wh ...[more]

PMID: 31871641

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Project description:Understanding broad-scale ecological patterns and processes often involves accounting for regional-scale heterogeneity. A common way to do so is to include ecological regions in sampling schemes and empirical models. However, most existing ecological regions were developed for specific purposes, using a limited set of geospatial features and irreproducible methods. Our study purpose was to: (1) describe a method that takes advantage of recent computational advances and increased availability of regional and global data sets to create customizable and reproducible ecological regions, (2) make this algorithm available for use and modification by others studying different ecosystems, variables of interest, study extents, and macroscale ecology research questions, and (3) demonstrate the power of this approach for the research question-How well do these regions capture regional-scale variation in lake water quality? To achieve our purpose we: (1) used a spatially constrained spectral clustering algorithm that balances geospatial homogeneity and region contiguity to create ecological regions using multiple terrestrial, climatic, and freshwater geospatial data for 17 northeastern U.S. states (~1,800,000 km2); (2) identified which of the 52 geospatial features were most influential in creating the resulting 100 regions; and (3) tested the ability of these ecological regions to capture regional variation in water nutrients and clarity for ~6,000 lakes. We found that: (1) a combination of terrestrial, climatic, and freshwater geospatial features influenced region creation, suggesting that the oft-ignored freshwater landscape provides novel information on landscape variability not captured by traditionally used climate and terrestrial metrics; and (2) the delineated regions captured macroscale heterogeneity in ecosystem properties not included in region delineation-approximately 40% of the variation in total phosphorus and water clarity among lakes was at the regional scale. Our results demonstrate the usefulness of this method for creating customizable and reproducible regions for research and management applications.

Dataset Information

Silhouette width using generalized mean-A flexible method for assessing clustering efficiency.

Publications

Silhouette width using generalized mean-A flexible method for assessing clustering efficiency.

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